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Velocity distribution on the membrane of a tank-treading red blood cell

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Abstract

The kinematics of an area-conserving tank-treading disk-shaped red blood cell membrane is studied using the stream function method suggested by Secomb and Skalak (Q. Jl Mech. appl. Math. 35, Pt 2, 233–247, 1982). Two simple area-conserving velocity fields are superimposed to satisfy the continuity condition at the curved edges of the disk. A differential equation for the trajectory of any material point of the membrane is derived. The requirement of synchrony of the cycle for all membrane points leads to an integral equation which determines a magnitude function. An approximate solution is made possible by assuming small trajectory deflections.

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Literature

  • Chien, S., S. S., Feng, M. Vayo, L. A. Sung, S. Usami and R. Skalak. 1988. “The Dynamics of Shear Disaggregation of Red Blood Cells in a Flow Channel.”Biorheology, submitted.

  • Evans, E. A. and R. Skalak. 1980.Mechanics and Thermodynamics of Biomembranes. Boca Raton, FL: CRC Press.

    Google Scholar 

  • Feng, S. S. 1988. “Red Blood Cells Tank-Treading in a Simple Shear Flow.” Doctoral Thesis, Columbia University.

  • Fung, Y. C. 1981.Biomechanics. New York: Springer.

    Google Scholar 

  • Secomb, T. W. and R. Skalak, 1982. “Surface Flow of Viscoelastic Membrane in Viscous Fluid.”Q.J. Mech. appl. Math. 35, Pt 2, 233–247.

    MATH  Google Scholar 

  • Skalak, R. 1976.Microcirculation, J. Grayson and W. Zingg (Eds), New York: Plenum Press.

    Google Scholar 

  • —, A. Tozeren, P. R. Zarda and S. Chien. 1973. “Strain Energy Functions of Red Blood Cell Membrane.”Biophys. J. 13, 245–264.

    Article  Google Scholar 

  • Tran-Son-Tay, R. 1983. “A Study of the Tank-Treading Motion of Red Blood Cells in Shear Flow.” Washington University, St. Louis, MO.

    Google Scholar 

  • Vayo, M. 1986. “Theoretical and Experimental Analysis of Shear Disaggregation of Red Blood Cell Rouleaux.” Doctorial Thesis, Columbia University.

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Authors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Columbia University, 10027, New York, NY, USA

    Si-shen Feng & Richard Skalak

  2. Department of Physiology and Cellular Biophysics, Columbia University, 10032, New York, NY, USA

    Shu Chien

Authors
  1. Si-shen Feng
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  2. Richard Skalak
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  3. Shu Chien
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Feng, Ss., Skalak, R. & Chien, S. Velocity distribution on the membrane of a tank-treading red blood cell. Bltn Mathcal Biology 51, 449–465 (1989). https://doi.org/10.1007/BF02460083

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  • DOI: https://doi.org/10.1007/BF02460083

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